Final answer:
The n-th term of the sequence 18, 27, 36, 45, 54 is 9n + 9.
Step-by-step explanation:
To find the n-th term of the given sequence 18, 27, 36, 45, 54, we can observe that each term is obtained by adding 9 to the previous term. To determine the nᵗʰ term of a given sequence, we must first ascertain the pattern of the sequence.
Looking at the sequence 18, 27, 36, 45, 54, we notice that each term is increasing by a constant difference. Let's find this common difference: 27 - 18 = 9 36 - 27 = 9 45 - 36 = 9 54 - 45 = 9 The common difference (d) is 9. This indicates that the sequence is arithmetic, meaning each term is obtained by adding the common difference to the previous term.
Now let's find the first term (a₁) of the sequence, which is simply the first number in the sequence, 18. An arithmetic sequence can be expressed using the formula
: aₙ = a₁ + (n - 1)d Where: - aₙ is the nᵗʰ term of the sequence - a₁ is the first term of the sequence - n is the position of the term in the sequence - d is the common difference between the terms Plugging in the values we know: aₙ = 18 + (n - 1)9 We can simplify this to: aₙ = 18 + 9n - 9 Further simplifying, we get: aₙ = 9n + 9 Thus, the nth term (aₙ) of the sequence 18, 27, 36, 45, 54 is: aₙ = 9n + 9 This formula will give us the desired term of the sequence for any position n.
So, the common difference between each term is 9.
Therefore, the formula to find the n-th term of an arithmetic sequence is Tₙ = T₁ + (n-1)d, where Tₙ is the n-th term, T₁ is the first term, n is the position of the term, and d is the common difference.
Applying this formula to the given sequence, Tₙ = 18 + (n-1)9 = 9n + 9